Is it legal to have a video camera at a Major league baseball game?

Yes, Major League Baseball does permit you to bring a video camera into a ball park and you are allowed to use it to record as long as it doesn't interfere with other fans or the enjoyment of the current game that's being played however some ballparks may not allow you to bring in Tripods or camera bags. Progressive Field, the home park of the Cleveland Indians does not allow fans to enter with Tripods but video cameras are permitted.

Turner Field allows the use of video cameras but no game action being recorded is permitted.